init

FOTF Toolbox/gershgorin.m

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+function gershgorin(H,key)
+% gershgorin - draw Nyquist plots with Gershgorin bands
+%
+%   gershgorin(H,key)
+%
+%   H - the frequency response data in FRD format
+%   key - if key=1, the inverse Nyquist plots are drawn
+   
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+if nargin==1, key=0; end
+t=[0:.1:2*pi,2*pi]'; [nr,nc]=size(H); nw=nr/nc; ii=1:nc; 
+for i=1:nc, circles{i}=[]; end
+for k=1:nw  % evaluate inverse Nyquist array for the frequencies
+   G=H((k-1)*nc+1:k*nc,:); 
+   if nargin==2 && key==1, G=inv(G); end, H1(:,:,k)=G;
+   for j=1:nc, ij=find(ii~=j);
+      v=min([sum(abs(G(ij,j))),sum(abs(G(j,ij)))]);
+      x0=real(G(j,j)); y0=imag(G(j,j));
+      r=sum(abs(v)); % compute Gershgorin circles radius
+      circles{j}=[circles{j} x0+r*cos(t)+sqrt(-1)*(y0+r*sin(t))];
+end, end
+hold off; nyquist(tf(zeros(nc)),'w'); hold on; 
+h=get(gcf,'child'); h0=h(end:-1:2); 
+for i=ii, for j=ii
+   axes(h0((j-1)*nc+i)); NN=H1(i,j,:); NN=NN(:);
+   if i==j  % diagonal plots with Gershgorin circles
+      cc=circles{i}(:);  x1=min(real(cc)); x2=max(real(cc)); 
+      y1=min(imag(cc)); y2=max(imag(cc)); plot(NN) 
+      plot(circles{i}), plot(0,0,'+'), axis([x1,x2,y1,y2])
+   else, plot(NN), end    % non-diagonal elements
+end, end, hold off
+if key==1, title('Inverse Nyquist Diagram'); end